Do I have ownership of my private keys?

Yes! Using the BTC.com wallet, you are the owner of your private keys. BTC.com never has access to your Bitcoin / Bitcoin Cash. You get access to your private keys in the form of a seed. This seed backs up all your private keys with the corresponding public keys at once.

How does it affect me?

It means that nobody can stop you from moving your funds out of the wallet e.g. we can’t freeze your wallet. It also means that if you lose your backup document and forget your password, we can’t help you regain access. You are your own bank, and you are in charge of your wallet’s security.